The appearance of oscillatory flows within a horizontal packed bed partly heated from below

We report on a numerical investigation of the unsteady mixed convective flow in a channel through a horizontal porous layer under localised isothermal heating from below to probe the oscillatory flow and thermal characteristics. The study was carried out for water flow within a plane channel containing stainless steel spherical particles. For this study, the channel height/particle diameter ratio was H/d=100 and the porosity was epsilon = 0.35. The effects of the imposed pressure-driven flow characterised by the P & eacute;clet number (0.1 <= Pe <= 1000), and heating represented by the Rayleigh number (105 <= Ra <= 2 x 107), are investigated. The results reveal that for low P & eacute;clet numbers, steady free convective flows are dominant, while for high P & eacute;clet numbers, steady forced convective flows dominate. Importantly, no oscillatory flows are found to develop in the free and forced convection regimes. However, for moderate P & eacute;clet numbers, oscillatory mixed convective flows occur with different periodic, quasi-periodic, and chaotic flow behaviours. In addition, for low Rayleigh numbers, Ra <= 10(6), the Nusselt number is not influenced by the P & eacute;clet number for Pe <= 1. Nevertheless, for high Rayleigh numbers, Ra >= 2 x10(6), it is observed that there always exists a critical P & eacute;clet number for which the Nusselt number is a minimum. The effects of the P & eacute;clet and Rayleigh numbers on the local and average temperature disparity between the fluid and solid phases are then investigated.